A circle has a radius of $5$. An arc in this circle has a central angle of $\dfrac{1}{5}\pi$ radians. What is the length of the arc? ${10\pi}$ ${\dfrac{1}{5}\pi}$ $\color{#DF0030}{1\pi}$ ${5}$
Solution: First, calculate the circumference of the circle. $c = 2\pi r = 2\pi (5) = 10\pi$ The ratio between the arc's central angle $\theta$ and $2 \pi$ radians is equal to the the ratio between the arc length $s$ and the circle's circumference $c$ $\dfrac{\theta}{2 \pi} = \dfrac{s}{c}$ $\dfrac{1}{5}\pi \div 2 \pi = \dfrac{s}{10\pi}$ $\dfrac{1}{10} = \dfrac{s}{10\pi}$ $\dfrac{1}{10} \times 10\pi = s$ $1\pi = s$